By Johansen S., Ramsey F.L.
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Extra resources for Bang-Bang representation for 3 on 3 embeddable stochastic matrices
After appropriate non-dimensionalizations, there are two non-dimensional parameters appearing in the diﬀerential equations. One is the ratio of the relaxation times of ψ and A, the other, known as the Ginzburg–Landau parameter, is the ratio of the characteristic lengths over which ψ and A vary. These two length scales are referred to as the coherence and penetration lengths respectively. In this paper, we consider a simpliﬁed Ginzburg–Landau system for ψ in which A is assumed to be a given vector-valued ﬁeld.
1 respectively. In Sect. 2, we describe a renewed version of the approach  to the 2D elliptic (Calderon) problem. As is shown, to recover a Riemann surface from its Dirichlet-to-Neumann (DN) map is to determine the crown of a certain function algebra, determined by the DN map, on the boundary. In Sect. 3, a hyperbolic dynamical system with boundary control is introduced. Such a system can be realized in the canonical form so that the realization possesses the features of “intuitive hyperbolicity:” its states propagate into a compact set with ﬁnite speed.
P possesses a cyclic element in H. 4. Exhausting property. PσT = I for all σ. Property 1 is principal: the continuously extending reachable sets correspond to the intuitive image of the waves propagating with ﬁnite speed. 3 can be applied to. Property 4 is rather technical and is accepted just for the sake of simplicity: it describes the case where the waves propagate into a bounded domain and exhaust the inner space for suﬃciently large times. In addition, we note that, by continuity, each eikonal T ξ dPσξ τσ = 0 has a purely continuous spectrum ﬁlling the segment [ 0, τσ ] ⊆ [0, T ].